Evaluating a Definite
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Calculus of a Single Variable
- Fill-in the blank. Evaluating the integral f +x+1 dx equals (x + _+ C) x2 +1arrow_forwardUse the Fundamental Theorem of Calculus, Part I to find the area of the region under the graph of the function f(x) = 16 cos(x) on 0, . %3D (Use symbolic notation and fractions where needed.) A = %3Darrow_forwardArea Function a) Find the formula for the area function, A(x), represented by the integral. b) Use that formula to find both A(t) and A(2t). c) Graph f(t) = sin (;t) and shade the area for the interval [0, 27]. d) Graph A(x) on the same graph and plot the point (2r, A(2n)). e) What is the relationship between parts (c) and (d)? sin dtarrow_forward
- Use the Fundamental Theorem of Calculus, Part I to find the area of the region under the graph of the function f(x) = 2x2 on %3D [0, 2]. (Use symbolic notation and fractions where needed.) %3Darrow_forwardSetup an integral to find the area inside the graph of r = 2-2sin(theta) and outside the graph of r = 3.arrow_forwardState Green's Theorem as an equation of integrals, and explain when Green's Theorem applies and when it does not. Give an example of Green's Theorem in use, showing the function, the region, and the integrals involved. 4.arrow_forward
- Determine the area bounded by f(x)=x²-x and x- axis. A - unit² B unit² с unit² D -unit² 3 +|5 w|marrow_forwardusing the fundamental theorem of calculus, calculate the area by hand for the intervals belowarrow_forwardDetermine the area of the shaded region bounded by y = -x² +6x and y=x² - 2x. The area of the region is (Type an exact answer.) Ayarrow_forward
- Evaluate the integral using the Fundamental Theorem of Calculus, Part I. (Use symbolic notation and fractions where needed.) 5 dxarrow_forwardDetermine the area bounded by f(x) = x² - X and x-axis. 2 A -unit² B -unit² C unit² Ⓒ un D unit²arrow_forwardLet R be an area bounded by the function f (x) = x above and g (x) x4 below. What is the area of the area R?|arrow_forward
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